关键词: 煤柱岩爆, 弹性地基, 折迭突变模型, 能量输入率, 稳定性判别, 等效刚度

Abstract: Under the condition of considering unexcavated coal seams as an elastic ground base, this paper deduces the equation of rock beam’s deflection line using the symbolic operation software—Maple 9.5. Then it deduces the equilibrium equation for the rock beam-coal pillar system when the system deforms in a quasi-static way, which is the equilibrium equation of fold catastrophe model. The discrimination of stability by using total potential energy function of fold catastrophe shows that, the system of rock beam and coal pillar is in an unstable equilibrium state in premonitory phase of rockburst, and critical condition of rockburst in coal pillar is Cook’s stiffness criterion. The criterion can be expressed dynamically that, the required energy input rate of the environment approaches to zero while the deformation of coal pillar increases. The releasing amount of earthquake energy is calculated; and it is clarified that the mechanism of rockburst in coal pillar is that the elastic energy released by rock beam exceeds the energy dissipated by the deformation of coal pillar with softening characteristics after peak value. The obtained findings is described by the geometric form in which the curves of energy input rate, rate of change of rock beam’s elastic energy and dissipated energy of coal pillar are given. Calculations show that, the stiffness coefficient of unexcavated coal bed has faint influence on the rock beam’s equivalent stiffness. The excavation of working surface and the increment of exhausted area lessen rock beam’s equivalent stiffness remarkably.

Key words: rockburst in coal pillar, elastic foundation, fold catastrophe model, energy input rate, discrimination of stability, equivalent stiffness